A Laboratory Model for the Parker Spiral and Magnetized Stellar Winds

ARTICLES https://doi.org/10.1038/s41567-019-0592-7 A laboratory model for the Parker spiral and magnetized stellar winds Ethan E. Peterson 1*, Douglass A. Endrizzi 1, Matthew Beidler2,3, Kyle J. Bunkers 1, Michael Clark1, Jan Egedal1, Ken Flanagan 1, Karsten J. McCollam1, Jason Milhone 1, Joseph Olson 1, Carl R. Sovinec 2, Roger Waleffe 1, John Wallace1 and Cary B. Forest1 Many rotating stars have magnetic fields that interact with the winds they produce. The Sun is no exception. The interaction between the Sun’s magnetic field and the solar wind gives rise to the heliospheric magnetic field—a spiralling magnetic structure, known as the Parker spiral, which pervades the Solar System. This magnetic field is critical for governing plasma processes that source the solar wind. Here, we report the creation of a laboratory model of the Parker spiral system based on a rapidly rotating plasma magnetosphere and the measurement of its global structure and dynamic behaviour. This laboratory system exhibits regions where the plasma flows evolve in a similar manner to many magnetized stellar winds. We observe the advec- tion of the magnetic field into an Archimedean spiral and the ejection of quasi-periodic plasma blobs into the stellar outflow, which mimics the observed plasmoids that fuel the slow solar wind. This process involves magnetic reconnection and can be modelled numerically by the inclusion of two-fluid effects in the simulation. The Parker spiral system mimicked in the laboratory can be used for studying solar wind dynamics in a complementary fashion to conventional space missions such as NASA’s Parker Solar Probe mission. n 1958, Eugene Parker first predicted the existence of the dominant plasma forces change in nature. These three interfaces supersonic solar wind1, which was subsequently verified by are the transonic, trans-Alfvénic and trans-β zones1,11,12. They char- Iearly spacecraft missions2,3. He also theorized how this solar acterize where the solar wind speed becomes supersonic, where it wind interacts with the dynamo-generated magnetic field of the becomes super-Alfvénic (inertial forces dominate magnetic forces, Sun—carrying the magnetic field lines away from the star, while that is VAlfven B=pμ0min<Vsw), and where the plasma pressure ¼ 2 their footpoints are frozen into the corona and twisted into an overcomesI the magnetic pressure (that is, β = 2μ0nT/B > 1), respec- Archimedean spiral by stellar rotation. This magnetic topology is tively. These transitionffiffiffiffiffiffiffiffiffiffiffiffi zones depend on the magnetic field strength now known as the Parker spiral and is the largest magnetic struc- B, the plasma density n, the plasma temperature T, the ion mass ture in the heliosphere. The transition between the magnetic field mi and the local solar wind speed Vsw. As a result, the transitions co-rotating with a star and the field advected by the wind is thought are governed by the interaction between the magnetic topology of to occur near the so-called Alfvén surface, where inertial forces in the Sun and the plasma acceleration and heating mechanisms in the wind can stretch and bend the magnetic field. According to the corona. This interaction results in complex, often overlapping, the governing equations of magnetohydrodynamics (MHD), this transition zones that vary wildly with heliographic latitude as well transition in a magnetic field like that of the Sun is singular in as heliocentric distance and give rise to the wide range of character- nature and therefore suspected to be highly dynamic4,5. However, istics exhibited by the solar wind13,14. this region has rarely been observed in situ by spacecraft and is Many spacecraft missions since the early 1960s have been dedi- presently the primary focus of the Parker Solar Probe mission6,7. cated to observing and categorizing the composition, speed, density Here we show, in a synergistic approach to studying solar wind and magnetic field of the solar wind from various vantage points dynamics, that the large-scale magnetic topology of the Parker spi- to gain insight into the origins and acceleration of the solar wind15. ral can also be created and studied in the laboratory. By generating Possibly none of these missions is more famous than Ulysses, which a rotating magnetosphere with Alfvénic flows, magnetic field lines was the first to fly over the solar poles and discovered that the are advected into an Archimedean spiral, giving rise to a dynamic ‘fast’ solar wind tends to come from the open field lines of coronal current sheet that undergoes magnetic reconnection and plasmoid holes, whereas the ‘slow’ solar wind has its origins in the equatorial ejection. These plasmoids are born near the Alfvén surface, at the streamer belt16. However, the mechanisms that transport the slow tip of the helmet streamer, and carry blobs of plasma outwards at solar wind plasma from closed field lines in the streamer belt to super-Alfvénic speeds, mimicking the dynamics of unstable coro- the open field lines of the Parker spiral are more ambiguous and nal helmet streamers, which are thought to fuel a significant por- have motivated theoretical, computational and observational work tion of the slow solar wind8–10. dedicated to elucidating this issue5,17–20. Despite the fundamental As the solar wind evolves from the lower corona to 1 au, the gov- role these dynamical interfaces play in the origin and evolution erning dynamics change dramatically as the plasma is accelerated of the solar wind, they have received little experimental attention. outward and the magnetic field of the Sun decreases. The solar wind Nevertheless, a laboratory model of this system is not only possible, experiences three primary dynamical interfaces—regions where the but provides new insight into the behaviour of dynamical interfaces 1Department of Physics, University of Wisconsin–Madison, Madison, WI, USA. 2Engineering Physics Department, University of Wisconsin–Madison, Madison, WI, USA. 3Present address: Oak Ridge National Laboratory, Oak Ridge, TN, USA. *e-mail: [email protected] NATURE PHYSICS | www.nature.com/naturephysics ARTICLES NATURE PHYSICS a Virtual c Separatrix Anodes Helmholtz coil 3D Hall sensor array B cathode φ LaB6 cathodes 2D mach and triple probes J φ JR B φ SmCo dipole b 15 ) –1 10 VA Vφ (km s 5 V VR Mo 0 anodes 0 0.2 0.4 0.6 0.8 R (m) Fig. 1 | A laboratory recipe for creating a Parker spiral and stellar wind. a, Drawing current from anodes in the plasma atmosphere to a virtual cathode in the magnetosphere creates a cross field current JR and associated torque on the plasma. b, This torque drives plasma rotation, shown by the toroidal velocity Vφ (green solid line). The rotation becomes super-Alfvénic at the radius denoted by the star when the rotation speed surpasses the Alfvén speed, VA (blue dash-dotted line). This super-Alfvénic rotation launches a radial wind shown by VR (orange dashed line). This wind then stretches the magnetic field lines outwards while they are twisted into a spiral by rapid rotation, forming the magnetic structures shown in a. This evolution produces a separatrix between the closed and open flux surfaces—a characteristic that is universal to many magnetized winds, and the understanding of which is vital to the study of stellar momentum transport and evolution. The experimental procedure to create the Parker spiral system is described in more detail in the Methods. c, Schematic of the experiment. relevant to the evolution of stellar winds, with special attention The remainder of this Article presents the measurements of this given to the dynamics near the Alfvén and β = 1 surfaces. laboratory Parker spiral, demonstrating three major findings: (1) In this Article, we report the creation of a laboratory model of the magnetic field is advected into an Archimedean spiral, (2) the the Parker spiral system and the measurement of its global struc- associated current sheet is dynamic and produces plasmoids near ture and dynamic behaviour. This system is realized by produc- the Alfvén radius, (3) these plasmoids travel outwards at super- ing a rotating plasma magnetosphere whose magnetic topology Alfvénic speeds and can be understood through the lens of Hall- evolves from a closed magnetosphere into an Archimedean spi- MHD. For comparison to the dynamics of the solar wind, Table 1 ral. We show that this system develops interface regions where outlines some dimensionless parameters relating this experiment in V ≈ VAlfvén and β ≈ 1, which become highly dynamic and result in the BRB to the solar wind. Although this laboratory system cannot processes that transport plasma from closed dipolar flux surfaces reflect the scale of the heliosphere, has no appreciable gravitational out to the open field lines of the Parker spiral. The experiments are effects, has a constrained return current path and does not produce compared to two-dimensional (2D) extended magnetohydrody- supersonic flows, it nevertheless recreates the macroscopic topology namic (MHD) simulations performed with the NIMROD code21, of stellar magnetic fields like the Parker spiral and its interactions which convincingly show that two-fluid (Hall) effects are essential with Alfvénic plasma flows. for understanding the current sheet and flows that develop. These We begin, for context, by summarizing the time dynamics of a experiments were carried out in the Big Red Ball (BRB) device at shot sequence as shown in Fig. 2. Important to note are the two the Wisconsin Plasma Physics Laboratory (WiPPL)22. The BRB, distinct phases present, which are characterized by an initial, non- shown in Fig. 1c, is a versatile 3-m-diameter multi-dipole con- axisymmetric state with large broadband fluctuations (phase I) and finement device capable of confining high-ionization-fraction, an axisymmetric, coherent, unstable state (phase II). A snapshot unmagnetized plasmas, and is well suited for investigations of basic of visible light captured by a fast camera during each of these two plasma systems and phenomena.

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